Parametric Life Cycle Assessment of Nuclear Power for Simplified Models

Electrifying the global economy is accepted as a main decarbonization lever to reach the Paris Agreement targets. The IEA’s 2050 Net Zero transition pathways all involve some degree of nuclear power, highlighting its potential as a low-carbon electricity source. Greenhouse gas emissions of nuclear power reported in the life cycle assessment literature vary widely, from a few grams of CO2 equivalents to more than 100 g/kWh, globally. The reasons for such a variation are often misunderstood when reported and used by policymakers. To fill this gap, one can make LCA models explicit, exploring the role of the most significant parameters, and develop simplified models for the scientific community, policymakers, and the public. We developed a parametric cradle-to-grave life cycle model with 20 potentially significant variables: ore grade, extraction technique, enrichment technique, and power plant construction requirements, among others. Average GHG emissions of global nuclear power in 2020 are found to be 6.1 g CO2 equiv/kWh, whereas pessimistic and optimistic scenarios provide extreme values of 5.4–122 g CO2 equiv/kWh. We also provide simplified models, one per environmental impact indicator, which can be used to estimate environmental impacts of electricity generated by a pressurized water reactor without running the full-scale model.


Functional unit
Process-based LCA is an ISO-standardized method for assessing the environmental impacts of a product or a service.More specifically, the ISO14040/44 standards define the processes to follow in order to account for all flows of energy and materials, emissions and waste, linked directly or indirectly to a so-called "functional unit".This functional unit is strictly defined to represent (non-exhaustively) either a service provided, the use of a product, the activity of a territory over a given period, or the deployment of a technology.
In the present case, the functional unit can be defined as "generating 1 kWh of high-voltage electricity from a pressurized water reactor".The nuclear reactor and uranium fuel chain are modelled to be representative of the 2020 global situation (or the most recent year available).The system associated with this functional unit is represented in Figure S1.

Data collection
Nuclear power has been subject to a consultation process with the World Nuclear Association in order to build new life cycle inventories for the front-end, core, and back-end processes of the nuclear life cycle.Significant changes have been brought to the nuclear power inventory in Gibon et al. [1] regarding the mining & milling (using Haque et al. [2] as main source for this step), and spent fuel management, which reflects recent changes in the nuclear power industry.

Uranium extraction
Data for the extraction of uranium was collected from the IAEA's UDEPO database, which contains grade-tonnage data for all operational uranium extraction sites in the world.Although the IEAE does not communicate on the exact mine-level data, a graphical representation of the database is available on Figure S2.The retained distribution is lognormal, with mean 0.1544% and standard deviation 0.1299%, as reported in Monnet et al. [3].

Figure S2. Uranium ore grade range with respect to tonnage, per mine. Available at https://infcis.iaea.org/UDEPO/Chart
The global extraction technique mix has significantly evolved between 1998 and 2021 (Figure S3), ISL dominates the uranium production market with two-thirds of the global production for that last year.This mode shift has consequences on the life cycle environmental profile of nuclear fuel as ISL has for example a lower GHG footprint than other techniques [2].In the present model, the share of ISL in the mining mix is retained as a parameter, with the open pit and underground mining shares rescaling accordingly.In the absence of a proper technology description, other extraction techniques are aggregated into the "open pit" category.
Figure S4 shows how energy requirements vary with ore grade and extraction technique for 23 data points [2,[5][6][7][8][9].The correlation is weak, but the general trend is that energy use tends to decrease with increasing ore grade.For ISL, this decrease is very slow, which can be interpreted by the fact that this technique does not require to move an amount of waste rock proportional to ore grade, unlike the two others.Outliers include [8], showing that only 53 MJ of energy is necessary to the open cast extraction of 1 kg U3O8 at 0.15%, or 440 MJ/kg U3O8 via ISL, more than double the next-highest value.In general, more data points are required to reduce the uncertainty of this parameter before a solid interpretation can be made.Regarding energy inputs of mining, the retained values are shown in Table S1, Table S2, Table S3, and Table S4.For comparison, values form the various sources available is shown in Table S5 and Table S6.

Conversion
In the conversion step, yellowcake undergoes several processes: dissolution in nitric acid, solvent extraction, washing, and concentration by evaporation.The resulting solution is then calcined to produce uranium trioxide or dioxide.This uranium oxide is then combined with gaseous hydrogen fluoride in a kiln to produce uranium tetrafluoride (UF4), which finally reacts with gaseous fluorine (F2) to produce uranium hexafluoride (UF6).Because of the kiln, conversion is a heat-intensive process, and requires about 600 MJ of energy per kg UF6 [11], this heat input is kept as a parameter.Conversion generates low-level radioactive waste, 90% of which is directed to interim storage, while 9% is incinerated (plasma torch) and 1% is surface or trench-deposited, as assumed in [11].The original model assumes the same shares, with the plasma torch incineration being modelled on the Zwilag treatment plant in Würenlingen, Switzerland 1 .Radioactive emissions from the waste treatment were adjusted from 1.66 and 3.04 GBq/m 3 of carbon-14 and tritium, respectively (1993 data) to 0.04 and 8.40 GBq/m 3 (2017 data, from [12], assuming a constant throughput of waste, i.e. 5 m 3 /year).

Enrichment
Two main technologies used to dominate the uranium enrichment market: gaseous diffusion, and centrifugation.Both techniques exploit the difference of molecular mass between 235 U and 238 U to achieve separation and increase the enrichment rate (of 235 U, the fissile isotope) of the product.As the molecular masses of the two isotopes is minuscule (about 0.4%), enrichment is an energy-intensive process.The unit conventionally used to quantify the amount of enrichment work, used to separate enriched (product) and depleted (tails) uranium from an instream (feed) of natural uranium is the "separative work unit" (SWU).
Enrichment processes involve the separation of a feed of UF6 into two outputs with different 235 U/ 238 U isotope concentrations, the enriched product and the depleted tails.Depending on the feed assay (the original concentration), the desired enrichment rate and the tails assay, a centrifuge, or more likely an array thereof, will provide a variable amount of work.Following Glaser [13], we write the mass balance of the enrichment process as: We use the notations of [13] where , , and  are the feed, product, and tails streams, typically in kg/year, and   are the respective fraction of the fissile material 235 U, in each stream.We define the cut  as the proportion of the feed exiting the process as product, i.e.  = .It can be shown that the cut is dependent on the various rates   , and is therefore fixed for a given configuration.The work (energy) needed to enrich or deplete a flow is defined through the function (), which obeys the following equation: Where  is the separative power for producing quantity P from quantity F. There is no exact analytical expression for () but using Taylor series, its second derivative can be estimated, from which () is given the standard expression: Combining the two latter equations, the amount of SWU per enriched material can be computed as   , which after simplification yields the following expression: This value is used in the life cycle inventories.
Depending on the actual technique used, the energy value of a SWU can span from about 40 kWh/SWU for gas centrifugation, to more than 2 MWh/SWU in gas diffusion techniques.Here, The feed contains the natural 235 U content of 0.71%, tails are usually about 0.22%; with these parameters 1 SWU could enrich fuel to about 1.41%.

Construction
The construction phase contains only a single parameter, which scales all of material flows up or down in the same proportion.The dependence between the intensity in material inputs can be explained by the fact that more cables would require simultaneously more steel, aluminum and copper, a thicker reactor containment building would require simultaneously more concrete and reinforcing steel, etc.

Operation
As the key component of nuclear fuel is the 235 U content, the relationship between burnup rate and enrichment should be approximately linear, but long-term studies show that high variations can be found between the two quantities.Hu et al. [19] show that fuel burnup and enrichment rate have concomitantly and steadily increased over the 1968-2013 period in US reactors, but without a strict linear relationship between the two, for the following reasons: nonroutine reactor operations (e.g.premature shutdown of reactors), leaking fuel rods prematurely replaced, or the fact that assemblies used in test programs can allow burnup rates higher than what is achievable under normal operations.Burns et al. [20] propose a linear model for burnup-enrichment relationship, with a slope of 10.9 GWd/tU per % of enrichment, i.e., the enrichment range commonly found in most fuel assemblies of 3%-5% would yield 32-54 GWd/tU respectively -which is retained for the model.The overall thermal efficiency of nuclear power plants spans over a much narrower range, usually around 33%, as found in the literature survey.It is kept as a parameter nonetheless.

A note on ionizing radiation
When ionizing radiation is considered, radon-222 emissions and radiation integration time are highly significant.Ionizing radiation is an indicator seldom assessed, or at least analyzed in detail in LCA.The latest characterization factors were published by Frischknecht et al. [23], relying on a 1995 report [24], using the so-called "linear no-threshold" (LNT) model that assumes that human health impacts occur from the first radionuclide emissions.Although conservative and precautionary, this LNT model has been criticized as no effects of radiation have been discerned under 100 mSv of received dose [29].As life cycle impact assessment is by construction linear, it suffers the same criticism.Similarly, the question of integration time raises the question of whether radionuclide emissions will still be of concern to humanity in 80000 years (when climate change commonly uses a 100-year horizon).

Figure S5 .
Figure S5.Bulk material requirements for a nuclear power plant, in tons per GW of nameplate capacity.

Figure S6 .
Figure S6.Relationship between discharge burnup rate and enrichment rate, following the model ofBurns et al.  [20].

Table S13 .
Inputs for encapsulation of spent fuel from interim storage, per TWh of NPP operation....

Table S1 .
Inputs for surface, open pit mining, per kg of uranium in ore.

Table S2 .
Inputs for underground mining, per kg of uranium in ore.

Table S3 .
Inputs for surface mining, in-situ leaching, per kg of U in yellowcake.

Table S4 .
Inputs for milling, per kg of uranium in yellowcake.

Table S5 .
Inputs for uranium (underground & open pit) mining and milling

Table S6 .
Inputs for uranium (ISL) mining and

Table S8 .
Inputs for fuel fabrication, per kg fuel element.

Table S15 .
Life cycle impact assessment categories."Thecharacterization factor for human toxicity impacts (human toxicity potential) is expressed in comparative toxic units (CTUh), the estimated increase in morbidity in the total human population, per unit mass of a chemical emitted, assuming equal weighting between cancer and noncancer due to a lack of more precise insights into this issue.Unit: [CTUh per kg emitted] = [disease cases per kg emitted]" 2 "The characterization factor for aquatic ecotoxicity impacts (ecotoxicity potential) is expressed in comparative toxic units (CTUe), an estimate of the potentially affected fraction of species (PAF) integrated over time and volume, per unit mass of a chemical emitted.

Table S16 .
Simplified models, explaining 80% of the overall variance, with enrichment technique set to 100% centrifugation.